There are several different eschatological (end-times) perspectives in Protestant Christianity, including the following:

Amillennialists - end times prophecies are largely figurative

Post-tribulationists - the rapture will not occur until the end of the tribulation

Mid-tribulationists - the rapture will occur 3.5 years into the tribulation

Pre-tribulationists - the rapture will occur prior to the tribulation.

What is the eschatological view of the LDS church? Is it one of these or something different altogether? From what teaching does it arise--the Bible, the Book of Mormon, the Pearl of Great Price, the Doctrines and Covenants, or something else?

The rapture is the catching away of believers, which is believed by some to be taught in 1 Thessalonians 4:13

The tribulation is the 7 year period of time of great trouble, spoken of in Revelation.

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The chronology adopted by Latter-day Saint interpreters (and heavily grounded in LDS scripture) most closely approaches what you would call mid- or post-tribulationist. (That terminology is not current in Mormonism, in any case, nor is rapture: LDS prefer to say "those caught up to meet Christ", which is closely tied in with the return of the city of Zion, and talk also of the trials and wickedness of the last days without attaching a specific phrase to the suffering.)

D&C 88 is a good source for the LDS doctrine on the last days, among others:

For not many days hence and the earth shall tremble and reel to and fro as a drunken man; and the sun shall hide his face, and shall refuse to give light; and the moon shall be bathed in blood; and the stars shall become exceedingly angry, and shall cast themselves down as a fig that falleth from off a fig tree.

[more Revelation-type disasters]

And there shall be silence in heaven for the space of half an hour; and immediately after shall the curtain of heaven be unfolded, as a scroll is unfolded after it is rolled up, and the face of the Lord shall be unveiled;

And the saints that are upon the earth, who are alive, shall be quickened and be caught up to meet him.

This is followed, in this chronology, by the sounding of other trumps, presumably analogous to those of Revelation (although this is not explicit in the text). One distinction that is made is that as Jesus Christ returns with the City of Zion, the faithful are caught up to meet him, and together they return to the earth (rather than ascending to heaven). This is preliminary to the millennial reign of Jesus Christ over the whole earth, as a key theme of Mormonism is the sanctification and elevation of this earth to celestial status, rather than relegating it to destruction.

There are a lot of popular LDS books which discuss hypothetical timelines, but officially there is no clear position taken on the order of events in the last days---only that prophecy will be fulfilled. Other major LDS sources on the last days are D&C 45, 101, 133, and Joseph Smith's translation/version of Matthew in the Pearl of Great Price. The Book of Mormon is conspicuously silent on this point, if I recall correctly, with the exception of few messianic Isaiah quotations and the confirmation that a Second Coming is to be expected. The Gospel Principles manual chapters 43 and 44 are a good place to look for more information as well.